Question: Find the greatest common factor of $16, 27,$ and $20$.
Explanation: The greatest common factor (GCF) is the largest number that is a factor of $16, 27,$ and $20$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}16 &=2\cdot2\cdot2\cdot2\\\\\\\\ 27&=3\cdot3\cdot3\\\\\\\\ 20&=2\cdot2\cdot5 \end{aligned}$ Since these numbers have no common prime factors, we say that the GCF is $1$. This is because all numbers share a factor of $1$ : $ \begin{aligned}16 &=2\cdot2\cdot2\cdot2\cdot1\\\\\\\\ 27&=3\cdot3\cdot3\cdot1\\\\\\\\ 20&=2\cdot2\cdot5\cdot1 \end{aligned}$ The greatest common factor of $16, 27,$ and $20$ is $1$.